Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains a temporally balanced set of \(G\) observations. First, the data set limited to plots that meet our plot-based filtering criteria (see below). Then the data set was further restricted to plots with at least 2 \(G\) observations (i.e., three FIA tree census records), with one in each of the two following decades: 2000-2010 (including censuses part of FIA 3.0 from 1996-2000 as part of the 2000 panel), and 2011-2022. For plots that had >2 \(G\) observations we took the first and last ones.

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset:

  • The data set has 108135 observations, comprised of 56950 plots.
  • The frequency of growth measurements among plots is as follows : 25737, 14117, 14220, 2876.
  • Thus 54.81 % of plots have at least two growth intervals.

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   4784     3418.7                               
## 2   4783     3416.0  1   2.645   3.703 0.05437 .  
## 3   4782     3247.2  1 168.863 248.679 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17365.95
## 2     2 17364.25
## 3     3 17123.56
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.131469   0.160885   0.817    0.414    
## phi    0.006572   0.004971   1.322    0.186    
## alpha  0.616728   0.036756  16.779   <2e-16 ***
## A      3.649488   0.116422  31.347   <2e-16 ***
## k     10.037803   0.836798  11.995   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.824 on 4782 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.59e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   4782     3247.2                              
## 2   4781     3241.5  1 5.7127  8.4260 0.003716 **
## 3   4781     3241.9  0 0.0000                    
## 4   4780     3241.4  1 0.5820  0.8582 0.354289   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17123.56
## 2    3a 17117.14
## 3    3b 17117.87
## 4    3c 17119.01
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.137026   0.161038   0.851  0.39487    
## phi    0.006114   0.004963   1.232  0.21811    
## alpha  0.614478   0.036736  16.727  < 2e-16 ***
## A      3.727638   0.125186  29.777  < 2e-16 ***
## k     16.050720   2.946710   5.447 5.38e-08 ***
## p      0.191531   0.056536   3.388  0.00071 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8234 on 4781 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 4.944e-07
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96731, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -14.161, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 178 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 178 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1256 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  11749    10574.1                                
## 2  11746    10532.7  3  41.39  15.388 5.469e-10 ***
## 3  11745     9879.3  1 653.45 776.861 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 41749.19
## 2     2 41699.80
## 3     3 40949.23
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.460005   0.143695   3.201  0.00137 ** 
## phi    0.027073   0.003893   6.954 3.75e-12 ***
## alpha  0.825898   0.027194  30.371  < 2e-16 ***
## A      2.990195   0.081105  36.868  < 2e-16 ***
## k     13.849194   0.647205  21.398  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9171 on 11745 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.043e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  11745     9879.3                                 
## 2  11744     9778.5  1 100.817 121.082 < 2.2e-16 ***
## 3  11744     9804.4  0   0.000                      
## 4  11743     9777.6  1  26.841  32.236 1.398e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 40949.23
## 2    3a 40830.70
## 3    3b 40861.83
## 4    3c 40831.61
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.441431   0.141982   3.109  0.00188 ** 
## phi    0.027381   0.003866   7.082  1.5e-12 ***
## alpha  0.816236   0.027055  30.170  < 2e-16 ***
## A      3.243761   0.097183  33.378  < 2e-16 ***
## k     29.321917   2.662420  11.013  < 2e-16 ***
## p      0.196126   0.014537  13.491  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9125 on 11744 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.614e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 449 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 449 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1316 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   5443     6161.6                               
## 2   5442     6160.8  1   0.807   0.7127 0.3986    
## 3   5441     5911.9  1 248.898 229.0731 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23135.70
## 2     2 23136.99
## 3     3 22914.40
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.443517   0.090979 -15.866   <2e-16 ***
## phi   -0.006224   0.005391  -1.155    0.248    
## alpha  0.680400   0.042432  16.035   <2e-16 ***
## A      6.575548   0.196248  33.506   <2e-16 ***
## k     22.072484   2.179249  10.128   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.042 on 5441 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.265e-06
##   (8 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5441     5911.9                                
## 2   5440     5858.0  1 53.833  49.991 1.739e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 22914.40
## 2    3a 22866.58
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.473531   0.089253 -16.510  < 2e-16 ***
## phi    -0.005956   0.005362  -1.111  0.26671    
## alpha   0.679421   0.041892  16.218  < 2e-16 ***
## A       8.471464   0.599656  14.127  < 2e-16 ***
## k     135.622939  36.052377   3.762  0.00017 ***
## p       0.333113   0.022074  15.091  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.038 on 5440 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.561e-06
##   (8 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 184 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 187 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1236 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   3266     2821.2                               
## 2   3265     2817.2  1   3.96   4.5898 0.03224 *  
## 3   3264     2607.6  1 209.68 262.4609 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 12271.84
## 2     2 12269.24
## 3     3 12018.42
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.100789   0.226876  -0.444   0.6569    
## phi    0.020776   0.009551   2.175   0.0297 *  
## alpha  0.832225   0.046720  17.813   <2e-16 ***
## A      4.708312   0.214756  21.924   <2e-16 ***
## k     31.488631   2.393785  13.154   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8938 on 3264 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.782e-06
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3264     2607.6                                
## 2   3263     2547.8  1 59.728  76.494 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 12018.42
## 2    3a 11944.66
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.133943   0.221239  -0.605   0.5449    
## phi     0.018025   0.009345   1.929   0.0538 .  
## alpha   0.824110   0.046217  17.831  < 2e-16 ***
## A       6.281777   0.438152  14.337  < 2e-16 ***
## k     112.639376  18.441855   6.108 1.13e-09 ***
## p       0.178895   0.012828  13.945  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8836 on 3263 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.181e-06
##   (5 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92606, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.765, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 136 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 141 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1279 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6131     6669.8                                 
## 2   6130     6658.8  1  11.004   10.13  0.001466 ** 
## 3   6129     6463.6  1 195.226  185.12 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24830.44
## 2     2 24822.31
## 3     3 24641.79
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.407158   0.093170  -15.10  < 2e-16 ***
## phi   -0.022515   0.007102   -3.17  0.00153 ** 
## alpha  0.651389   0.045068   14.45  < 2e-16 ***
## A      7.147056   0.251328   28.44  < 2e-16 ***
## k     50.686599   3.984017   12.72  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.027 on 6129 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.344e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 24641.79
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.407158   0.093170  -15.10  < 2e-16 ***
## phi   -0.022515   0.007102   -3.17  0.00153 ** 
## alpha  0.651389   0.045068   14.45  < 2e-16 ***
## A      7.147056   0.251328   28.44  < 2e-16 ***
## k     50.686599   3.984017   12.72  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.027 on 6129 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.344e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 228 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 228 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1298 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8164      24852                                 
## 2   8163      24788  1   64.67  21.296 3.995e-06 ***
## 3   8162      23018  1 1769.84 627.581 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 45299.06
## 2     2 45279.79
## 3     3 44676.79
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.913956   0.101905  -8.969  < 2e-16 ***
## phi   -0.033783   0.006375  -5.300 1.19e-07 ***
## alpha  0.904581   0.032985  27.424  < 2e-16 ***
## A      7.183336   0.188407  38.127  < 2e-16 ***
## k      4.264530   0.502079   8.494  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.679 on 8162 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.73e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8162      23018                                
## 2   8161      22955  1 62.655 22.2754 2.402e-06 ***
## 3   8161      22957  0  0.000                      
## 4   8160      22954  1  2.663  0.9466    0.3306    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 44676.79
## 2    3a 44656.53
## 3    3b 44657.03
## 4    3c 44658.09
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.926217   0.101199  -9.152  < 2e-16 ***
## phi   -0.033728   0.006358  -5.305 1.16e-07 ***
## alpha  0.901351   0.032809  27.472  < 2e-16 ***
## A      7.423544   0.214506  34.608  < 2e-16 ***
## k     11.260249   2.763059   4.075 4.64e-05 ***
## p      0.337129   0.056220   5.997 2.10e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.677 on 8161 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.924e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 319 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 319 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1255 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7978      25296                                 
## 2   7977      25249  1   46.28  14.622 0.0001324 ***
## 3   7976      23598  1 1651.45 558.183 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43252.71
## 2     2 43240.09
## 3     3 42702.23
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.681866   0.128007  -5.327 1.03e-07 ***
## phi   -0.034515   0.006578  -5.247 1.58e-07 ***
## alpha  0.888852   0.033928  26.198  < 2e-16 ***
## A      6.628775   0.215241  30.797  < 2e-16 ***
## k     11.166431   0.920464  12.131  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.72 on 7976 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.048e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7976      23598                                 
## 2   7975      23443  1 155.023  52.737 4.173e-13 ***
## 3   7975      23484  0   0.000                      
## 4   7974      23440  1  43.892  14.931 0.0001124 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 42702.23
## 2    3a 42651.63
## 3    3b 42665.68
## 4    3c 42652.74
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.688250   0.126957  -5.421 6.10e-08 ***
## phi   -0.034467   0.006538  -5.272 1.39e-07 ***
## alpha  0.879204   0.033729  26.067  < 2e-16 ***
## A      7.109710   0.263661  26.965  < 2e-16 ***
## k     27.822440   4.517425   6.159 7.68e-10 ***
## p      0.256828   0.028256   9.089  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.715 on 7975 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.537e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 312 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 312 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1239 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    828     2612.6                                 
## 2    827     2612.6  1   0.013  0.0041    0.9489    
## 3    826     2484.7  1 127.904 42.5193 1.218e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4460.386
## 2     2 4462.382
## 3     3 4422.670
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.460303   1.392394   1.049  0.29459    
## phi   -0.009615   0.029538  -0.326  0.74488    
## alpha  0.866396   0.119147   7.272 8.25e-13 ***
## A      4.007083   0.896530   4.470 8.93e-06 ***
## k     12.599203   4.384869   2.873  0.00417 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.734 on 826 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.068e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': p
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    826     2484.7                            
## 2    825     2470.1  1 14.651  4.8934 0.02723 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4422.670
## 2    3a 4419.755
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.284095   1.306800   0.983  0.32608    
## phi   -0.006035   0.029574  -0.204  0.83836    
## alpha  0.863186   0.119111   7.247 9.80e-13 ***
## A      4.476783   1.042824   4.293 1.97e-05 ***
## k     43.646726  33.869703   1.289  0.19788    
## p      0.360039   0.119863   3.004  0.00275 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.73 on 825 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.67e-07
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8582, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.819, p-value = 0.004817
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 33 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 33 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1212 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1260     1094.2                                 
## 2   1259     1093.1  1  1.1063  1.2742 0.2591949    
## 3   1258     1082.1  1 11.0489 12.8453 0.0003513 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4656.943
## 2     2 4657.665
## 3     3 4646.834
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.65627    0.30592  -2.145 0.032123 *  
## phi    0.01046    0.01288   0.812 0.417208    
## alpha  0.40995    0.10959   3.741 0.000192 ***
## A      4.19172    0.32018  13.092  < 2e-16 ***
## k     23.47473    4.02493   5.832 6.94e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9274 on 1258 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.683e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1258     1082.1                                
## 2   1256     1035.5  2 46.579  28.249 9.987e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4646.834
## 2    3a       NA
## 3    3b       NA
## 4    3c 4595.262
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.70808    0.29077  -2.435   0.0150 *  
## phi     0.01065    0.01258   0.847   0.3971    
## alpha   0.43472    0.10329   4.209 2.75e-05 ***
## A       9.21966   12.33472   0.747   0.4549    
## k     323.67972  599.31168   0.540   0.5892    
## s       1.60302    0.94592   1.695   0.0904 .  
## p       0.26034    0.36495   0.713   0.4758    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.908 on 1256 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 9.084e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9178, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.508, p-value = 7.616e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 48 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 48 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1306 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    104     285.83                            
## 2    103     277.64  1 8.1866  3.0371 0.08437 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1       NA
## 2     2 379.8761
## 3     3 378.7376
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge     11.4402    91.7591   0.125   0.9010  
## phi     0.2633     0.1960   1.343   0.1822  
## alpha   1.4472     0.7272   1.990   0.0492 *
## A       0.2025     1.1221   0.181   0.8571  
## k       7.0363    12.0122   0.586   0.5593  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.642 on 103 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.911e-06

summary

  • simple model: does not fit
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    103     277.64                           
## 2    102     277.56  1 0.080696  0.0297 0.8636
##   model      AIC
## 1     3 378.7376
## 2    3a 380.7062
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge     11.4402    91.7591   0.125   0.9010  
## phi     0.2633     0.1960   1.343   0.1822  
## alpha   1.4472     0.7272   1.990   0.0492 *
## A       0.2025     1.1221   0.181   0.8571  
## k       7.0363    12.0122   0.586   0.5593  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.642 on 103 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.911e-06

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88675, p-value = 1.502e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.58007, p-value = 0.5619
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1366 row(s) containing missing values (geom_path).

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)  
## 1    127     112.40                            
## 2    126     112.13  1 0.26844  0.3016 0.5838  
## 3    125     109.08  1 3.04756  3.4922 0.0640 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 421.2904
## 2     2 422.9796
## 3     3 421.3975
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2726     1.7336   0.157   0.8753  
## A    4.1582     1.7879   2.326   0.0216 *
## k  101.1654    45.1400   2.241   0.0268 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9408 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.017e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    127      112.4                         
## 2    126      111.9  1 0.5007  0.5638 0.4541
##   model      AIC
## 1     1 421.2904
## 2    1a 422.7100
## 3    1b 423.2902
## 4    1c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2726     1.7336   0.157   0.8753  
## A    4.1582     1.7879   2.326   0.0216 *
## k  101.1654    45.1400   2.241   0.0268 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9408 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.017e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87973, p-value = 7.476e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.3275, p-value = 0.01994
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_pointrange).
## Warning: Removed 1288 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5077     3443.2                                 
## 2   5076     3434.0  1   9.208  13.611 0.0002273 ***
## 3   5075     3214.7  1 219.349 346.286 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18143.10
## 2     2 18131.50
## 3     3 17798.18
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.760791   0.197570   3.851 0.000119 ***
## phi   0.009542   0.004535   2.104 0.035417 *  
## alpha 0.636808   0.031873  19.980  < 2e-16 ***
## A     2.977392   0.110237  27.009  < 2e-16 ***
## k     3.767706   0.519220   7.256 4.57e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7959 on 5075 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.728e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   5075     3214.7                              
## 2   5074     3210.2  1 4.4803  7.0815 0.007813 **
## 3   5074     3213.0  0 0.0000                    
## 4   5073     3207.6  1 5.3515  8.4636 0.003639 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17798.18
## 2    3a 17793.10
## 3    3b 17797.48
## 4    3c 17791.02
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.764045   0.197642   3.866 0.000112 ***
## phi    0.009677   0.004542   2.130 0.033180 *  
## alpha  0.638591   0.031785  20.091  < 2e-16 ***
## A      2.920319   0.109849  26.585  < 2e-16 ***
## k     16.881030   3.542011   4.766 1.93e-06 ***
## p      0.553707   0.066927   8.273  < 2e-16 ***
## s      1.993079   0.535678   3.721 0.000201 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7952 on 5073 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 7.509e-06

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 175 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 175 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5337      11963                                 
## 2   5336      11916  1  47.468  21.256 4.111e-06 ***
## 3   5335      11670  1 245.864 112.397 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 26768.05
## 2     2 26748.82
## 3     3 26639.49
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.164602   0.124921  -9.323  < 2e-16 ***
## phi   -0.035378   0.008384  -4.220 2.49e-05 ***
## alpha  0.793374   0.070937  11.184  < 2e-16 ***
## A      6.020186   0.221308  27.203  < 2e-16 ***
## k     11.354119   2.234415   5.081 3.87e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.479 on 5335 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.631e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 26639.49
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.164602   0.124921  -9.323  < 2e-16 ***
## phi   -0.035378   0.008384  -4.220 2.49e-05 ***
## alpha  0.793374   0.070937  11.184  < 2e-16 ***
## A      6.020186   0.221308  27.203  < 2e-16 ***
## k     11.354119   2.234415   5.081 3.87e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.479 on 5335 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.631e-06

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 204 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 204 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1226 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    597     820.19                                 
## 2    596     820.18  1  0.0117  0.0085    0.9267    
## 3    595     797.12  1 23.0609 17.2136 3.827e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2462.209
## 2     2 2464.201
## 3     3 2449.089
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.17229    1.41660   1.533   0.1257    
## phi   -0.01169    0.03025  -0.386   0.6994    
## alpha  0.87551    0.19632   4.460 9.82e-06 ***
## A      2.32697    0.49213   4.728 2.83e-06 ***
## k     19.88285    9.06806   2.193   0.0287 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.157 on 595 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.277e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2449.089
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.17229    1.41660   1.533   0.1257    
## phi   -0.01169    0.03025  -0.386   0.6994    
## alpha  0.87551    0.19632   4.460 9.82e-06 ***
## A      2.32697    0.49213   4.728 2.83e-06 ***
## k     19.88285    9.06806   2.193   0.0287 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.157 on 595 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.277e-06

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95126, p-value = 3.563e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.084988, p-value = 0.9323
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 21 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1311 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    663     866.92                                
## 2    662     854.80  1 12.120  9.3866  0.002275 ** 
## 3    661     829.09  1 25.702 20.4908 7.107e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2729.245
## 2     2 2721.868
## 3     3 2703.536
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.10198    1.56501   1.343  0.17970    
## phi    0.06479    0.02892   2.241  0.02539 *  
## alpha  0.80384    0.16677   4.820 1.78e-06 ***
## A      2.13854    0.49961   4.280 2.14e-05 ***
## k      9.61180    3.71444   2.588  0.00987 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.12 on 661 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 9.664e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2703.536
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.10198    1.56501   1.343  0.17970    
## phi    0.06479    0.02892   2.241  0.02539 *  
## alpha  0.80384    0.16677   4.820 1.78e-06 ***
## A      2.13854    0.49961   4.280 2.14e-05 ***
## k      9.61180    3.71444   2.588  0.00987 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.12 on 661 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 9.664e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94157, p-value = 1.62e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1287, p-value = 2.917e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 28 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 28 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_pointrange).
## Warning: Removed 1324 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    289     237.80                                 
## 2    288     236.89  1  0.9123  1.1091    0.2932    
## 3    287     218.47  1 18.4208 24.1990 1.466e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 824.5545
## 2     2 825.4321
## 3     3 803.7946
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.26208    1.70618  -0.154  0.87803    
## phi    0.03132    0.03808   0.823  0.41143    
## alpha  0.79043    0.14033   5.633 4.23e-08 ***
## A      2.55201    0.96322   2.649  0.00851 ** 
## k     35.96032   11.88470   3.026  0.00270 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8725 on 287 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.54e-06

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    287     218.47                          
## 2    286     218.38  1 0.09401  0.1231 0.7259
## 3    286     218.47  0 0.00000               
## 4    285     217.78  1 0.69081  0.9040 0.3425
##   model      AIC
## 1     3 803.7946
## 2    3a 805.6689
## 3    3b 805.7944
## 4    3c 806.8696
## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.26208    1.70618  -0.154  0.87803    
## phi    0.03132    0.03808   0.823  0.41143    
## alpha  0.79043    0.14033   5.633 4.23e-08 ***
## A      2.55201    0.96322   2.649  0.00851 ** 
## k     35.96032   11.88470   3.026  0.00270 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8725 on 287 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.54e-06

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92069, p-value = 2.49e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.3803, p-value = 0.1675
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 11 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1349 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3a
212 Laurentian Mixed Forest 3a
221 Eastern Broadleaf Forest 3a
222 Midwest Broadleaf Forest 3a
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3a
232 Outer Coastal Plain Mixed Forest 3a
234 Lower Mississippi Riverine Forest 3a
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3c
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 3
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3c
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4788 2394 0.1370256 -0.1786829 0.4527341 0.0061136 -0.0036171 0.0158443 0.6144777 0.5424585 0.6864969 3.7276384 3.4822166 3.973060 16.050720 10.273812 21.82763
212 Laurentian Mixed Forest east 11752 5876 0.4414314 0.1631222 0.7197406 0.0273810 0.0198026 0.0349595 0.8162358 0.7632041 0.8692675 3.2437614 3.0532673 3.434255 29.321917 24.103132 34.54070
221 Eastern Broadleaf Forest east 5454 2727 -1.4735313 -1.6485025 -1.2985600 -0.0059560 -0.0164676 0.0045556 0.6794207 0.5972956 0.7615457 8.4714639 7.2958986 9.647029 135.622939 64.945853 206.30002
222 Midwest Broadleaf Forest east 3274 1637 -0.1339434 -0.5677252 0.2998385 0.0180249 -0.0002985 0.0363483 0.8241103 0.7334938 0.9147267 6.2817773 5.4226971 7.140858 112.639376 76.480591 148.79816
223 Central Interior Broadleaf Forest east 6136 3068 -1.4071576 -1.5898037 -1.2245115 -0.0225150 -0.0364377 -0.0085923 0.6513886 0.5630393 0.7397379 7.1470562 6.6543658 7.639747 50.686599 42.876527 58.49667
231 Southeastern Mixed Forest east 8168 4084 -0.9262167 -1.1245924 -0.7278410 -0.0337276 -0.0461909 -0.0212642 0.9013512 0.8370363 0.9656661 7.4235438 7.0030571 7.844030 11.260249 5.843949 16.67655
232 Outer Coastal Plain Mixed Forest east 7982 3991 -0.6882500 -0.9371198 -0.4393803 -0.0344671 -0.0472838 -0.0216504 0.8792035 0.8130865 0.9453206 7.1097098 6.5928656 7.626554 27.822440 18.967107 36.67777
234 Lower Mississippi Riverine Forest east 832 416 1.2840954 -1.2809489 3.8491397 -0.0060349 -0.0640838 0.0520140 0.8631864 0.6293909 1.0969818 4.4767829 2.4298818 6.523684 43.646726 -22.834203 110.12766
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1264 632 -0.7080765 -1.2785284 -0.1376246 0.0106532 -0.0140195 0.0353260 0.4347183 0.2320868 0.6373498 9.2196578 -14.9792587 33.418574 323.679719 -852.082607 1499.44205
255 Prairie Parkland (Subtropical) pacific 418 209 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 108 54 11.4402262 -170.5423786 193.4228310 0.2632604 -0.1255003 0.6520211 1.4472251 0.0049288 2.8895215 0.2025387 -2.0228509 2.427928 7.036340 -16.787042 30.85972
332 Great Plains Steppe interior west 132 66 0.2725824 -3.1578627 3.7030275 NA NA NA NA NA NA 4.1581742 0.6202980 7.696051 101.165354 11.841451 190.48926
341 Intermountain Semi-Desert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 64 32 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5080 2540 0.7640445 0.3765809 1.1515081 0.0096770 0.0007724 0.0185817 0.6385909 0.5762783 0.7009035 2.9203194 2.7049685 3.135670 16.881030 9.937159 23.82490
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5340 2670 -1.1646020 -1.4094992 -0.9197049 -0.0353777 -0.0518142 -0.0189411 0.7933738 0.6543089 0.9324386 6.0201862 5.5863319 6.454040 11.354119 6.973753 15.73449
M223 Ozark Broadleaf Forest Meadow east 600 300 2.1722873 -0.6098501 4.9544247 -0.0116856 -0.0710982 0.0477269 0.8755140 0.4899461 1.2610818 2.3269709 1.3604411 3.293501 19.882849 2.073551 37.69215
M231 Ouachita Mixed Forest east 668 334 2.1019804 -0.9710094 5.1749702 0.0647916 0.0080089 0.1215742 0.8038450 0.4763735 1.1313164 2.1385430 1.1575385 3.119547 9.611801 2.318276 16.90533
M242 Cascade Mixed Forest pacific 40 20 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 12 6 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 292 146 -0.2620761 -3.6202910 3.0961387 0.0313211 -0.0436238 0.1062660 0.7904348 0.5142206 1.0666490 2.5520107 0.6561375 4.447884 35.960321 12.568097 59.35255
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 20 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 20 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  -0.3618113
## 2       pacific   0.0000000
## 3          east  -0.3873071
## 4 interior west   2.1570380

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US -0.005905188
## 2       pacific  0.000000000
## 3          east -0.006615666
## 4 interior west  0.067830119

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.7611072
## 2       pacific      0.0000000
## 3          east      0.7674957
## 4 interior west      0.6987496

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   5.614329
## 2       pacific   0.000000
## 3          east   5.686527
## 4 interior west   2.375343

K (stand biomass at half biomss G in Mg/ha)

##          region weighted.k
## 1     entire US   44.68927
## 2       pacific    0.00000
## 3          east   45.03369
## 4 interior west   44.42990